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The Role of Energy Capital in Accounting for
Africa’s Recent Growth Resurgence
Stephie Frieda
David Lagakos b
a
b
Carleton College
UCSD and NBER
January 31, 2017
Abstract
After decades of stagnation, Africa began a growth resurgence starting in around
2000. Over the same period, Africa made large investments in its stock of “energy capital,” and in particular its stock of electric power plants. We ask how much of Africa’s
recent growth resurgence can be accounted for by its investments in energy capital. To
answer this question we draw on a multi-sector model in which energy complements
labor and capital in the production of non-agricultural goods, and new cross-country
evidence on the stock of electric power plants. In our main specification, energy capital
investments account for around one third of Africa’s growth resurgence. This quantitative conclusion is driven by three features of the data: (i) Africa had extremely low
energy inputs per worker before 2000, (ii) its stock of energy capital and production of
energy increased robustly since then, and (iii) the share of energy in non-agricultural
production in Africa is substantial.
Email: [email protected], [email protected]. For helpful comments we thank Doug Gollin, Nick Ryan and
participants at IGC’s Growth Week conference. For excellent research assistance we thank Camila Gomes and
Shu Zhang. We are grateful to the IGC for financial support. All potential errors are our own.
1
1. Introduction
After decades of stagnation, Sub-Saharan Africa began a period of sustained GDP growth
starting in around 2000. According to national accounts data, annualized GDP growth
across African countries averaged six percent per year from 2000 to 2013. Over this period,
around two-thirds of Africans saw their nation’s GDP double. Moreover, most of Africa’s GDP
growth was associated with per capita income increases, rather than population growth.
For example in Africa’s two most populous countries, Nigeria and Ethiopia, GDP per capita
increased by 99 and 133 percent since 2000. Household surveys confirm Africa’s rapid
improvements in living standards, and, according to Young (2012), imply even faster rates
of growth than do the national accounts.
What are the main factors accounting for Africa’s growth? Providing a complete answer is
a challenging task, and beyond the scope of this paper.1 This paper focuses on the role of
one promising channel, which is the dramatic increase in energy capital, “energy capital,”
or capital goods that are used to produce electricity, made by many African countries since
2000. The most conspicuous examples include the numerous large-scale hydropower plants
being built in countries like Ethiopia, but much of the investments are more mundane, and
involve simply connecting more regions to the electricity grid.
Africa’s increases in energy capital have been accompanied by impressive growth in electricity production per capita, bringing Africa up from minuscule levels of electric power usage.
In 2000, the average African economy (excluding South Africa) averaged just 70 kilowatt
hours of consumption per capita per year. By comparison, the average U.S resident used
about this much in just two days. Since 2000, growth in Africa’s electricity production has
averaged 5.5 percent since 2000, roughly the same magnitude as its GDP growth. Moreover,
we show that across African countries, growth rates of manufacturing and service GDP are
strongly correlated with electricity growth, showing that the fastest growers are systematically the countries with the largest energy increases.
In this paper, we ask how much of Africa’s growth since 2000 can be accounted for by its
recent investments in energy capital. A key challenge we face is that growth in energy
1
One obvious candidate is a rise in commodity prices, which have driven up the value of Africa’s naturalresource exports. In the majority of African countries, however, we show that growth in manufacturing and
services GDP – excluding natural resources – has been just as dramatic as overall GDP growth. Nigeria and
Ethiopia have had manufacturing and services GDP growth averaging over 10 percent per year since 2000, for
example, to go along with their overall growth rate of 11 percent per year. Furthermore, some of the fastest
growth rates are found in countries (such as Ethiopia) which have negligible exports of natural resources (see
Radelet (2010)).
1
use and growth in GDP suffer from a classic chicken-and-egg problem, where each clearly
plays some role in causing the other. Pure econometric techniques to sorting our this twoway causality include, for example, instrumental variables that serve to assign one country
to more electricity investment than a second similar country. Finding such instrumental
variables at the country level is likely to be a difficult task; in any event, we don’t know of
any.
Instead, we take a structural approach to disciplining the size of the reverse-causality channel from income to electricity demand. To do so we draw on what is already known about
the income elasticity of demand for energy and other expenditure aggregates, using a multisectoral model in the spirit of Herrendorf, Rogerson, and Valentinyi (2014), and parameterized to match cross-sectional consumer expenditure patterns. In particular, we match the
increasing expenditure share on non-agricultural goods with income, which is standard in
the macro literature on structural change, and the increasing energy expenditure share with
income (see e.g. Wolfram, Shelef, and Gertler, 2012; Gertler, Shelef, Wolfram, and Fuchs,
2016). The model therefore quantitatively captures the direct effect of income on energy
demand and the indirect effect, working through increased demand for (energy-intensive)
non-agricultural goods.
On the production side, we follow Hassler, Krusell, and Olovsson (2015) and assume a
constant elasticity of substitution (CES) aggregate production function in two inputs: (i) a
Cobb-Douglas aggregate of labor and capital, and (ii) energy. Basically all macro models
of energy use agree that energy is strongly complementary to other inputs at an annual
frequency (Atkeson and Kehoe, 1999; Hassler, Krusell, and Olovsson, 2015; Hassler, Krusell,
and Smith, Jr., 2016).2 Using aggregate time series data from the United States, Hassler,
Krusell, and Olovsson (2015) estimate that the elasticity of substitution between energy
and the capital-labor composite at the annual level is close to zero. We follow them and
choose a low elasticity of substitution, though we show later than higher values also imply
a substantial role for energy investments in Africa’s growth, so long as the model matches
energy’s share of non-agricultural value added, which is around ten percent according to
African manufacturing censuses.3
2
This high degree of complementarity between sectoral inputs is emphasized by Jones (2011), who cites
electricity in particular as an example of a good with limited possibilities for substitution.
3
The reason Hassler, Krusell, and Olovsson (2015) find a low substitution elasticity for energy is that when
energy prices tripled in the 1970s, the energy input share in US production tripled as well, while quantities
of energy inputs remained roughly constant. The almost total lack of substitution away from energy in the
aggregate economy suggests very a low elasticity of substitution in the production function. Atalay (2015) uses
a similar strategy to argue that intermediate inputs in general are likely to have a low degree of substitution
with other inputs at business cycle frequencies.
2
We allow for two types of energy use in the model: grid and non-grid, which are imperfect
substitutes in the aggregate energy input. We assume that grid energy investment decisions are made exogenously by the government, and financed by lump-sum taxation on
households. Non-grid energy investments are chosen by households privately, and allow
households to produce their own energy in the absence of grid energy. Examples could be
an electric generator or solar panel purchased by a producer for the own use. The assumption that grid energy investment decisions are made by the government seems a reasonable
approximation to reality given that large-scale construction projects, such as hydroelectric
dams, are classic public goods, and nearly impossible to coordinate by private individuals.
However, the assumption that grid energy investments are financed by private citizens is a
less accurate description of reality, given substantial financing from development agencies
and foreign nations in practice, but is a convenient simplification and is not important for
our quantitative conclusions.
We discipline the importance of the two energy types in aggregate energy production in
the model using data on relative quantities and relative prices of grid and non-grid energy
constructed from micro evidence on energy capital use (Foster and Steinbuks, 2008). These
data show that non-grid energy is about five times as expensive as grid energy, and responsible for a much smaller fraction of total energy than grid energy. This implies that, in our
quantitative model, the private sector cannot easily provide their own energy at low cost.
We use the model to ask, counterfactually, how much Africa would have grown had it only
increased its (grid) energy investments, but experienced no other changes. In particular,
our main exercise is to increase energy investments so as to match the increases in energy
consumption since 2000, and to ask how much GDP per capita increases from this change
alone. We do this experiment country by country, for Africa’s six most populous countries,
for which data are readily available.
We find that energy investments account for around one third of Africa’s growth in GDP
per capita since 2000, on average. This substantial role for energy is due largely to three
basic features of the data. First, Africa had very low inputs of energy (that is, electricity, not
traditional sources like wood) per capita around 2000. Second, energy inputs increased substantially since 2000, at a rate of around eight percent per year on average. Third, the share
of energy in non-agricultural production is substantial, at around ten percent according to
several sources of data on manufacturing from Africa and other developing regions of the
world. We show that if any of these three features of the data were (counterfactually) not
present, the role of energy in accounting for Africa’s growth would have been substantially
3
smaller.
One caveat of our analysis is that we focus only on Africa’s six largest countries, due to data
availability. Other countries’ experiences may have been different, and in future work we
plan to address a larger set of countries to the extent possible. Perhaps a more important
caveat is that, even with the six countries studied at present, there is substantial variation
in our model’s predictive power across these countries. The model is least successful in
the Democratic Republic of Congo, where our model predicts essentially no role of energy
investments on growth since 2000. The Congo was mired in a destructive conflict in the
1990s, and grew since then for reasons likely out of the model. On the other end, in the Sudan and in Kenya, more than two-thirds of growth can be explained by energy investments,
according to the model. The reason is that both the Sudan and Kenya had large increases in
energy production, but with less dramatic GDP growth than the other countries. Among the
other countries – Ethiopia, Nigeria and Tanzania – energy investments account for between
23 and 31 percent, near the overall average of one third. Another caveat, which can be
made of almost any growth or development accounting paper, is that our findings are really
only “accounting” results, and don’t provide deeper answers as to why Africa made large
energy investments after 2000 and not before. We leave this important question to future
research.
Our paper is related to several micro studies that find clear positive impacts of energy investments on development. Lipscomb, Mobarak, and Barham (2013) study the development effects of electrification in Brazil from 1960 to 2000 using a geographic model of
hydropower plant placement to instrument for electricity grid expansion. They estimate
large effects of electricity on development metrics such as income, employment, housing
values and urbanization rates at the region level. Relatedly, Rud (2012) finds large positive
effects of electrification on manufacturing activity in particular, using panel data on Indian
regions from 1965 to 1984. Looking a shorter time horizon, Dinkelman (2011) uses the
land gradient to instrument for electrification at the regional level within South Africa from
1995 to 2001. She estimates increases in employment following electrification, particularly
for females, increases in male earnings, and increased migration towards regions getting
electrified.4
Our paper also contributes to a growing literature on the long-run macroeconomic effects of
4
Dinkelman and Schulhofer-Wohl (2015) argue that studying the effects of electrification (or other investments) on local areas will be misleading without accounting for the effects of internal migration. Our paper
is consistent with their view in that it focuses on the aggregate effects of energy investments, rather than just
regional effects.
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energy use. Many of these studies focus on the environmental impacts energy use; see e.g.
Golosov, Hassler, Krusell, and Tsyvinski (2014) and Hassler, Krusell, and Smith, Jr. (2016)
and the references therein. By contrast, our paper ignores environmental issues completely.
In Africa, several types of evidence suggest that this may be an innocuous omission. First,
most of Africa’s energy production (other than in South Africa) comes from hydropower,
which leads to minimal air pollution (see e.g. Eberhard, Rosnes, Shkaratan, and Vennemo,
2001). Second, manufacturing activity and automobile use are still at low levels compared
to the United States and other developed regions (Gertler, Shelef, Wolfram, and Fuchs,
2016). Our work adds to an extensive literature on growth accounting and development
accounting (i.e. accounting for level differences), though to our knowledge no other paper
has studied the role of energy capital separately from other capital inputs, or tried to account
for Africa’s recent growth.5
The remainder of this paper is structured as followed. Section 2 summarizes the facts on
Africa’s growth in GDP and energy inputs since 2000 that motivate this study. Section 3
presents a multi-sector general-equilibrium model that we use in our quantitative analysis.
Section 4 calibrates the model to match salient features of Africa’s most populous countries
around 2000, and Section 5 conducts the quantitative counterfactual experiments used to
quantify the role of energy investments in Africa’s growth. Finally, Section 6 concludes.
2. Africa’s Growth and Electricity Investments Since 2000
In this section we summarize Africa’s impressive growth in GDP, in electricity production
and consumption, and in electricity capital and since 2000. We then show that GDP growth
and electricity growth are strongly positively correlated across African countries.
2.1. Africa’s GDP Growth
Table 1 reports Sub-Saharan Africa’s average annual growth rate in the 1990s and since
2000. The differences are stark. On average, African countries grew at just 2.5 percent per
year in the 1990s, and at 6 percent from 2000 on. Countries growing at 5 percent percent
since 2000 (through 2013) have doubled their GDP over this period. Overall, there were just
five countries growing at a rate of 5 percent per year in the 1990s, compared to 16 countries
since 2000. Thus, since 2000, around two-thirds of Africans live in a country whose GDP
5
The papers by Klenow and Rodríguez-Clare (1997), Hall and Jones (1999) and Caselli (2005) are prominent examples in the development accounting camp, while Young (1995) s a prominent example in the growth
accounting camp.
5
has doubled. No period in African history has seen such drastic increases in living standards
for so many people.
Table 1: Economic Growth in Sub-Saharan Africa
1990s Since 2000
Annualized GDP Growth Rate
2.5
6.0
Countries with GDP Growth ≥ 5%
5
16
% of Population in Country w/ Growth ≥ 5%
14
66
Africa’s growth in per-capita terms has been impressive as well. Consider the most populous six countries in Africa (excluding South Africa), on which we will focus in this paper:
Nigeria, Ethiopia, the Democratic Republic of Congo, Tanzania, Kenya and Sudan. Since
2000, cumulative growth in GDP per capita averaged an astonishing 68.5 percent across
these countries, which amounts to 4.4 percent per year. Leading the pack were Ethiopia
at 133 percent cumulative growth in GDP per capita, or 7.1 percent per year, followed by
Nigeria, at 99 percent cumulative growth, or 5.7 percent per year.
What accounts for Africa’s robust recent growth in GDP? One natural candidate is an increase in the prices of natural resources that Africa tends to export. If this is the case, one
calls into question whether Africa’s GDP growth is informative about changes in living standards for the average Africans. After all, many natural resources are narrowly held or are
controlled by governments, who may or not use natural resource rents productively.
Figure 1 plots average annualized growth of GDP by broad sector in Africa’s six most populous countries (excluding South Africa). In each of these countries, growth in manufacturing
GDP and services GDP in quite similar to the overall GDP growth. In Nigeria, an oil exporter,
manufacturing and service GDP growth even exceed aggregate growth, at over ten percent
per year in both sectors. In Ethiopia, which has virtually no natural resource exports, the
service sector has had growth of over twelve percent per year, while manufacturing has had
growth of around nine percent per year, in the ballpark of the aggregate. These data show
plainly that African economic growth has been broad based, and is not a simple artifact of
rising prices of natural resources. See also Radelet (2010).
6
Figure 1: Average Annualized GDP Growth in Africa’s Largest Economies Since 2000
14 12 Percent 10 8 6 4 2 0 Nigeria Ethiopia GDP D.R. Congo Tanzania Manufacturing Kenya Sudan Services 2.2. Africa’s Electricity Production and Investments
One of the most impressive features of Africa’s growth has been its rapid increases in uses
of “modern” energy sources, in particular electricity. Most of Africa’s energy use currently
comes from “traditional” sources, such as burning wood or other biomass (International
Energy Agency, 2016). In 2000, modern energy use was at astonishingly low levels in most
African countries. Across Africa’s six largest countries, for example, electricity usage was
just 70 kWh per capita per year. Ethiopia had the lowest electricity inputs, at just 21 kWh
per capita per year. The average U.S. resident, as a comparison, used around 13,000 kWh
per year, or almost 200 times higher.
Since 2000, African economies have made substantial investments in modern energy capital. Figure 2 plots the annualized growth rate of energy capital and energy capital per capita
in the 1990s and in the 2000s, averaged across all Sub-Saharan Africa countries for which
7
data are available (excluding South Africa). To measure energy capital, we use megawatts
of electricity production capacity. The source for this data is the UDI World Electric Power
Plants Database, which is a global inventory of electric power generating units from 19702014.6 Energy capital per capita actually decreased on average in the 1990s, with an annualized growth rate of -0.61 percent. In contrast, during the 2000s, energy capital per
capita increased on average at an annualized rate of 2.58 percent per year, implying that
the average African economy saw its level of energy capital per capita grow by more than
fifty percent between 2000 and 2013.
Figure 2: Average Annualized Growth Rate of Energy Capital in Sub-Saharan Africa
6 5.49 5 Percent 4 3 2.58 2.18 2 1 0 -­‐0.61 Energy Capital per Capita -­‐1 Energy Capital 1990s 2000s Figure 3 plots the growth rate of energy capital per capita for the Democratic Republic of
6
Energy capital data are not available over the relevant time horizons for the following Sub-Saharan African
Countries: Benin, Botswana, Burkina Faso, Cote d’Ivoire, The Gambia, Guinea-Bissau, Equatorial Guinea,
Lesotho, Mauritania and Sudan.
8
the Congo, Ethiopia, Kenya, Nigeria, and Tanzania, five of the six African countries on which
we focus this paper (data on energy capital for Sudan are not available). Looking across
these five countries, Ethiopia clearly stands out with an average annualized growth rate of
energy capital per capita of 10.8 percent since 2000. Kenya and Nigeria also experienced
considerable increases in the growth rate of energy capital per capita since 2000. In contrast,
both the Democratic Republic of the Congo and Tanzania saw lower rates of growth in energy
capital per capita in the 2000s than in the 1990s.
Figure 3: Average Annualized Growth Rate of Energy Capital Per Capita By Country
12 10.8 10 8 Percent 6 3.6 4 2.1 2.0 2 1.9 2.1 Nigeria Tanzania 0 -­‐0.6 -­‐2 -­‐4 -­‐3.1 -­‐2.6 -­‐6 -­‐8 -­‐6.9 D.R. Congo Ethiopia Kenya 1990s 2000s The large increases in energy capital were accompanied by similarly large increases in energy production and consumption. Figure 4 plots the average annualized growth in electricity production and consumption since 2000. The y-axis is the same is for GDP in Figure
1 for comparison’s sake. As the figure shows, growth rates of electricity consumption are
similar in magnitude to those of GDP. In each of these countries, electricity consumption
exceeded GDP growth over this period. In Ethiopia, Sudan, Kenya and Tanzania, electric9
ity production increased by roughly as much or more than GDP per capita, as new power
plants and distribution lines were constructed. In Nigeria and the Congo, the story seems to
be more about reducing waste: net imports did not increase in Nigeria or the Congo since
2000, thus, the increase in electricity consumption without such a large increase in production must reflect lower fraction lost to theft or loss. In any case, each of these countries had
impressive increases in electric energy usage since 2000.
Figure 4: Avg. Annualized Electricity Growth in Africa’s Largest Countries Since 2000
14 12 Percent 10 8 6 4 2 0 Nigeria GDP Ethiopia D.R. Congo Electricity ConsumpEon Tanzania Kenya Sudan Electricity ProducEon Looking across countries, the data show that countries with the largest increases in electricity were also the ones that grew the most. Figure 5 plots manufacturing GDP growth
and electricity consumption growth since 2000 across all Sub-Saharan African countries for
which data are available. The 45-degree line is also plotted for expositional purposes. As
the figure shows, the correlation between the two variables is quite strong. The Spearman
correlation coefficient is 0.76, with a p-value of 0.001. When looking at overall GDP growth
or services GDP growth, the correlation coefficients are also quite high, at 0.63 and 0.64,
10
with p-values of 0.007 and 0.008. Of course, this correlation does not help separate the role
of electricity in driving growth from the increase in demand for electricity as GDP increases.
For this we turn to a model.
12
Figure 5: Manufacturing GDP Growth and Electricity Growth in Africa Since 2000
NGA
Manufacturing VA Growth Rate
0
3
6
9
ETH
COG
TZA
SDN
COD
BWA
ZMB
NAMKEN
GAB
ZAF
CMR
SEN
MUS
-3
ZWE
-3
0
3
6
Electricity Growth Rate
9
3. Model
In this section, we build a model to help us quantify the role of energy investments in Africa’s
robust growth in GDP per capita since 2000. Our basic approach is to discipline the income
elasticity of demand for energy directly in the model, in order to capture the channel leading
from income growth to energy demand. We then use the model to divide up growth in GDP
per capita into two parts: (i) that coming from energy investments, and (ii) that coming
from other exogenous factors.
11
3.1. Households and preferences
The economy is inhabited by a continuum of households of measure one. Each household is
endowed with one unit of labor which they supply inelastically to the labor market. Households can use their income to consume or to save.
Households divide their consumption among an agricultural good (e.g., food), Ca , a nonagricultural good, Cn , and energy, Ce . The non-agricultural good is the numeraire and
can be used to finance all three types of consumption. Empirically, the share of household
expenditures on agricultural falls as the income per capita rises and the economy undergoes
structural change (see e.g. Herrendorf, Rogerson, and Valentinyi, 2014). To ensure that our
model captures Engel’s Law, i.e. the negative relationship between income and agricultural
expenditure shares, we follow the structural change literature (e.g. Kongsamut, Rebelo, and
Xie, 2001) and assume that all households must consume a minimum “subsistence” level of
the agricultural good, ā.7
Lifetime utility is logarithmic over the three consumption goods,
∞
X
β t ωa log(Ca,t − ā) + ωn log(Cn,t ) + ωe log(Ce,t ) .
(1)
t=0
Parameters ωa , ωn and ωe denote the long-run expenditure shares of agriculture, nonagriculture, and energy, respectively.8 We require that these shares sum to unity: 1 = ωa +
ωn + ωe . As ā approaches zero, the logarithmic preferences imply that the elasticity of
substitution between each pair of consumption goods approaches unity.
Household save in physical capital. Following Greenwood, Hercowitz, and Krusell (1997),
we allow for separate levels of productivity for consumption goods and investment goods.
In particular, we assume that one unit of physical capital can be purchased from
1
q
units of
the non-agricultural good. Capital accumulates according to
K t+1 = (1 − δ)K t + qI t ,
7
(2)
Other specifications of non-homothetic preferences, such an additive utility term in non-agriculture (Laitner, 2000; Alvarez-Cuadrado and Poschke, 2011), or thresholds below which only agriculture is consumed
(Gollin, Parente, and Rogerson, 2002, 2007) would yield similar qualitative predictions. In future work we
plan to explore the model’s quantitative predictions under two recent specifications that allow for even more
flexibility in matching expenditure patterns (Boppart, 2014; Comin, Lashkari, and Mestieri, 2014).
8
We use the term long-run expenditure shares to refer to the expenditure shares in a country for which ā
represents a trivial amount of total consumption, such as the United States.
12
where parameter δ denotes the constant depreciation rate and I t is investment in terms of
non-agricultural goods. Households rent the capital to firms at rate R t .
3.2. Production technologies
Perfectly competitive firms produce the agricultural good, Ya , the non-agricultural good, Yn ,
and energy, E. We describe each production process in turn.
3.2.1. Agricultural good
The production technology for the agricultural good is Cobb-Douglas between capital, Ka ,
and labor, Na ,
θ
1−θ
Na,t
,
Ya,t = A t Ka,t
(3)
where θ denotes capital’s share and A is exogenous total factor productivity (TFP) in nonenergy production.
3.2.2. Non-agricultural good
Following the macro-energy literature (e.g., Hassler, Krusell, and Olovsson (2015)), the
production technology for the non-agricultural good features a constant elasticity of substitution, ε, between a capital-labor composite, Knθ Nn1−θ , and energy,
ε−1 ε
θ
1−θ ε−1
Yn,t = A t (1 − µ)(Kn,t
Nn,t
) ε + µEn,tε ε−1 ,
(4)
where µ is the distribution parameter between energy and the capital-labor composite.
3.2.3. Energy
Firms and households purchase an aggregate energy input, E t , from the final energy producer. The aggregate energy input is itself a Cobb-Douglas aggregate of two types of energy:
grid energy, E g t , and off-grid energy, Eot . Formally,
ρ
1−ρ
E t = Eot E g t ,
(5)
where parameter ρ denotes the share of off-grid energy in the energy aggregate.
In reality, these two inputs are meant to capture the fact that households and firms generally
13
have two sources for their electricity, and that the two sources are not perfect substitutes.
For example, while an off-grid solar system can easily power a light bulb or mobile phone,
it does not provide sufficient energy for a television, iron, or refrigerator, which are three
highly desirable appliances (see e.g. Lee, Miguel, and Wolfram, 2016). Similarly, an off-grid
generator can power a small number of sewing machines, but not an entire textile plant (see
e.g. Eberhard, Rosnes, Shkaratan, and Vennemo, 2001).
We model the production of grid and off-grid energy by two representative firms; one which
produces grid energy and one which produces off-grid energy. Each representative firm is
responsible for the generation of the electricity and for any required resource extraction
(such as coal mining). The main difference between the production of grid and off-grid
energy is that grid production uses public capital, K g , while off-grid production uses private
capital, Ko . Examples of this public capital include transmission lines, hydropower dams,
power stations and so forth.9 The respective production technologies for grid and off-grid
energy are
φ
1−φ
E g t = A g t K g t Ng t
and
φ
1−φ
Eot = Aot Kot Not
.
(6)
Parameter φ is capital’s share and A g and Ao denote exogenous TFP in grid and off-grid
energy production, respectively.
Since the grid capital is publicly provided, firms in the grid energy sector earn positive
profits, Π g , from energy production,
Π g = p g E g − wN g ,
(7)
where p g is the relative price of grid energy. The profits are returned to the household
through lump-sum transfers.
Our paper makes the strong assumption of perfect competition in electricity markets. Ryan
(2014) shows that in India, electricity prices and supply are governed by imperfect competition among electricity providers. To the extent that prices of electricity do not reflect
market value, this will affect our quantitative conclusions in several ways. We return to this
issue later.
9
Note that we are calling energy capital as something different from what Caselli (2015) calls natural
capital, and includes stocks of natural resources like diamonds, oil or land that is valuable for tourism.
14
3.3. Government
The government’s only role is to finance investment in grid capital. Like privately provided
capital, grid capital can be purchased from
1
q
units of the non-agricultural good and it de-
preciates at constant rate δ. The law of motion for grid capital is
K g,t+1 = (1 − δ)K g,t + qI g,t ,
(8)
where I g denotes government investment in grid capital. The government finances investment in grid capital through lump-sum taxes on the households, Tt .
3.4. Equilibrium
We define a stationary competitive equilibrium. Labor and private capital are perfectly
mobile across the sectors. The aggregate state variables are the level of private capital,
K = Ka + Kn + Ko , and the level of public capital, K g .
Given a level of grid energy investment, I g and levels of technological progress An , Aa ,
Ao and A g , a competitive equilibrium consists of households’ decision rules, {Ca , Cn , Ce , K 0 }
firms’ production plans, {Ka , Kn , Ko , Na , Nn , No , N g , En }, and prices {r, w, pa , pe , p g , po }, such
that the following holds:
1. Given prices, taxes, and grid-energy profits, households choose Ca , Cn , Ce and K 0 to
optimize equation (1) subject to the intertemporal budget constraint,
pa Ca + Cn + pe Ce +
K
K0
≤ w + RK + (1 − δ) + Π g − T
q
q
(9)
and the non-negativity constraints,
Ca ≥ 0,
Cn ≥ 0,
Ce ≥ 0
and
K 0 ≥ 0.
(10)
2. Firm demands for capital, labor, and energy satisfy:
r=
∂ (pa Ya ) ∂ Yn ∂ (po Eo )
=
=
∂ Ka
∂ Kn
∂ Ko
∂ (pa Ya ) ∂ Yn ∂ (po Eo ) ∂ (p g E g )
=
=
=
∂ Na
∂ Nn
∂ No
∂ Ng
∂ Yn
pe =
∂ En
w=
15
(11)
(12)
(13)
3. The government budget balances:
Ig = T
(14)
4. Markets clear:
E = En + Ce
(15)
K = Kn + Ko + Ka
(16)
N = Nn + No + Na + N g
(17)
0
‹
K 0 Kg
K Kg
+
= pa Ca + Cn + pe Ce + +
pa Ya + Yn + pe (E − En ) + (1 − δ)
q
q
q
q

(18)
4. Calibration
We analyze the effects of increases in grid electricity on economic growth in six of the
most populous countries in Sub-Saharan Africa: The Democratic Republic of the Congo,
Ethiopia, Kenya, Nigeria, Sudan, and Tanzania. We calibrate the model to match the average
characteristics of these countries in the pre-growth steady state, years 1986-2000.
We normalize non-energy TFP, A and grid-energy TFP, A g to unity: A = A g = 1. This amounts
to a choice of units. We take the values for six parameters, {ε,θ ,φ,δ,ωa ,ωn }, directly
from the data. We then calibrate the remaining parameters so that certain moments in the
model match their empirical values. Table 2 reports the calibrated parameter values and
their source. Subsections 4.1 and 4.2 describe direct calibration and method of moments
procedures, respectively.
16
Table 2: Parameter Values
Parameter
Model Value
Source
Production
Elasticity of substitution: ε
0.05
Distribution parameter: µ
1.46e-14
Hassler, Krusell, Olovsson (2015)
Method of moments
Capital share: θ
0.33
Capital’s share of income
Capital share in energy: φ
0.90
Capital’s share of energy production
Off-grid energy share: ρ
0.01
Method of moments
Depreciation rate: δ
0.04
Penn World Tables
TFP in non-energy: A
1
Normalization
TFP in grid energy: A g
1
Normalization
TFP in off-grid energy: Ao
0.05
Method of moments
Investment technology: q
0.52
Method of moments
Discount rate: β
0.96
Assumption
Weight on agriculture: ωa
0.02
Herrendorf, Rogerson, and Valentinyi (2014)
Weight on energy: ωe
0.04
U.S. expenditure share on energy
Weight on non-agriculture: ωn
0.94
1 − ωa − ωe
Subsistence consumption: ā
0.83
Method of moments
Preferences
Number of workers: N
1
Normalization
Government
Electricity investment: I g
0.01
Method of moments
4.1. Direct calibration
We calibrate the values for parameters, {ε,θ ,φ,δ,ωa ,ωn }, directly from the data. Parameter φ corresponds to capital’s share in the production of grid-energy. Producing grid-energy
requires both extracting the raw materials, such as coal or oil, and generating and transmitting electricity. Our model bundles these two components into a single, energy producing
firm. The empirical analog of our model’s grid-energy sector is thus, a combined sector
comprised of both resource extraction and power generation.10 The U.S. labor share in this
combined sector is 0.1, yielding a value of capital share for the production of grid energy
equal to 0.9.
10
The combined sector corresponds to NAICS codes 2211, 211, 2121, and 213 (power generation and supply,
oil and gas extraction, coal mining, and support activities for mining). Data on labor compensation are from
the BLS. Data on value-added are from the NIPA GDP-by-Industry accounts
17
The elasticity of substitution between the capital-labor composite and energy is a particularly prominent parameter in the macro-energy literature. Hassler, Krusell, and Olovsson
(2015) argue that this elasticity must be close to zero to replicate the historical movements
in energy share and energy prices in the US. Based on their evidence, we choose ε = 0.05,
the largest value that matches the historical data reasonably well.
The utility function weights, ωa , ωn , and ωe represent the respective consumption expenditure shares of agriculture, non-agriculture, and energy, in the special case when ā = 0.
Or, alternatively, when income is sufficiently high such that pa ā is small relative to total
consumption expenditures. Following the estimation used by Herrendorf, Rogerson, and
Valentinyi (2014), we set ωa = 0.02. We choose ωe = 0.038, the relative importance weight
on household energy consumption in 2015 U.S. Consumer Price Index (U.S. Bureau of Labor
Statistics, 2015). These two choices imply that ωn = 1 − ωa − ωe = 0.942.
We set the depreciation rate, δ, equal to 0.04, the average value from 1986-2000 across the
six Sub-Saharan Africa economies in our study (Feenstra, Inklaar, and Timmer, 2015). For
capital’s share in agriculture and in the capital-labor composite in the production of nonagriculture, we use the standard value of one third, θ = 0.33. For the discount factor, we
use the standard value of β = 0.96.
4.2. A method of moments
Given the directly calibrated parameter values, we choose the remaining six parameters,
{Ao ,µ,ρ, ā, I g ,q} to ensure that certain moments in the model match their values in the
data. While all six parameters are jointly determined, some moments are more important
for pinning down some parameters than others. We describe each parameter and its primary
moment in turn.
Parameter q determines the effectiveness with which agents can transform the non-agricultural
consumption good into capital. All else constant, economies that are better at creating capital goods (higher q) will have higher capital-output ratios. We choose q to target the average
capital-output ratio across the Sub-Saharan African economies in our study from 1986-2000
(Feenstra, Inklaar, and Timmer, 2015).
The value of off-grid TFP, Ao , determines determines the effectiveness with which capital
and labor can be used to produce off-grid energy relative to grid-energy. As Ao increases, the
marginal cost of producing off-grid energy falls, which, in turn, reduces the relative price of
off-grid energy. Estimates from Foster and Steinbuks (2008) suggest that off-grid energy is
approximately five times as expensive as grid energy in Sub-Saharan Africa (see Eberhard,
18
Rosnes, Shkaratan, and Vennemo, 2001, Figure 1.10 and Table A1.8.). We choose Ao to
target this relative price difference. Finally, I g determines the initial level of grid-energy
in the 2000 steady state. We choose this value to match the average ratio of (externally
financed) energy investment relative to GDP in the 1990s (Gutman et. al 2015).
Parameter µ primarily governs energy’s share of non-agricultural output. Estimating the
model analog of energy share in developing countries is particularly challenging because,
in many cases, the observed energy price does not reflect its true shadow value. Shortages
of electricity infrastructure combined with highly regulated pricing likely create substantial
excess demand for energy. Our model does not incorporate these market imperfections.
Therefore, the value of energy share we observe in the data is a lower bound on the value
that energy share would obtain, if the economy behaved according to our model with no
market imperfections. With this caveat in mind, we target the average energy share in the
manufacturing sector in Ethiopia. The average value of this share over years 1996-2000
(the years in the pre-growth period for which data is available) is 10 percent.11 Similar to
our value in Ethiopia, Allcott, Collard-Wexler, and O’Connell (2016) find that the average
energy share in Indian manufacturing is 11 percent.
The value of ρ, off-grid energy share in the production of the energy aggregate is pinned
down by the fraction of off-grid capital relative to total capital. Six percent of Sub-Saharan
Africa’s total generating capacity was from off-grid sources in 2006 (Foster and Steinbuks,
2008). Therefore, we choose ρ to target
Ko
K g +Ko
= 0.06. Parameter ā determines the relative
size of the agricultural sector. We choose ā such that the employment share in agriculture
is 0.67, the average value across Ethiopia, Nigeria, Sudan, and Tanzania, the four countries
for which data is available.
We use the Nelder-Meade simplex algorithm (Nelder and Mead, 1965) to minimize the
squared distance between the model and empirical values of the moments. The model fits
the moments quite closely; the minimized squared distance is 1.02 × 10−15 . Table 3 reports
the values of the moments we target in the model and their corresponding values in the
data. All moments match their targets to two decimal places or more.
How well does the model perform in matching moments not targeted directly? We first
compared the model’s predictions for the energy shares of expenditure in the model and
data from Africa. Eberhard, Rosnes, Shkaratan, and Vennemo (2001) report that Ethiopia’s
average budget share on energy in 2000 was 2 percent. The model predicts a value of 1
percent, which is not far off. Herrendorf, Rogerson, and Valentinyi (2014) report that the
11
Data from the Report on Large and Medium Scale Electricity and Manufacturing Survey, Table 3.7.
19
Table 3: Model Fit
Moment
Capital-output ratio
K
Y
Grid-electricity-investment-output ratio:
Share of Employment in Agriculture:
Electricity share of GDP:
pe E
Y
Fraction of off-grid capital:
Ko
Ko +K g
Price of off-grid to grid electricity:
po
pg
Na
N
Ig
Y
Data
Model
1.9
1.90
0.008
0.008
0.67
0.67
0.10
0.10
0.06
0.06
5.00
5.00
agriculture consumption share of GDP (Figure 6.9) is about 60 percent in African countries.
Our model predicts 72 percent. So this is reasonably comparable as well.
van Benthem (2015) report income elasticities of demand for energy (LDC category, Table
6). The average elasticity is 0.83. In the model, the elasticity is 1.96. Thus, the model’s elasticity is too large relative to the data. We note that this will render the model’s predictions
an under-estimate, since the model over-predicts the magnitude of the effect of income on
electricity demand, which in turn leads the model to under-predict the effect of energy on
income growth. In future work we plan to return to this issue.
Finally, we assess whether the model’s subsistence requirement is comparable with existing
evidence. In the model, the subsistence requirement is about 61 percent of GDP per capita
in Ethiopia in 2000. This corresponds to about $1.82 per day at PPP. This value is in the
same ballpark as the $1 per day and $2 per day thresholds for extreme poverty commonly
reported by the World Bank. We conclude that our subsistence term is reasonable given
these values.
5. Quantitative Counterfactual Exercises
Our goal is to estimate the contribution of expansions in grid energy infrastructure to growth
since 2000 in each of the six Sub-Saharan African economies in our study. We describe
the computational experiment for Ethiopia. The experiments for the other countries are
analogous.
20
5.1. Baseline Experiment
We begin the Ethiopian economy in its pre-growth steady state, calibrated according to
Section 4. We then calibrate a post-growth steady state which corresponds to year 2013,
the last year for which data on GDP and electricity consumption are available. Specifically,
we choose the values for non-energy TFP (A) and grid-energy investment (I g ) such that
the percent increase in GDP per capita and electricity per capita (measured in kilo watt
hours per capita) in the pre- and post-growth steady states match their observed increases
in Ethiopia between 2000 and 2013. By design, this post-growth steady state matches all of
the Ethiopian growth in output and grid-energy over the 2000-2013 period.
We also calculate a third, hypothetical, steady state in which only grid-energy infrastructure
grows; non-energy TFP remains at its pre-growth level. The three steady states are summarized in Table 4. We use the superscripts pr e and post to denote the pre- and post-growth
steady state values of A and I g . The pre-growth values of A and I g are the values reported
in Table 2 in Section 4.
Table 4: Computational Experiment
Steady State
Non-Energy TFP
Grid-Energy Investment
pr e
Pre-growth (year 2000)
pr e
A= A
Ig = Ig
Post-growth (year 2013)
A = Apost
Ig = Ig
Hypothetical
A = Apr e
Ig = Ig
post
post
To evaluate the importance of grid-energy infrastructure for Ethiopia’s growth, we compare
the increase in GDP per capita between the pre-growth and hypothetical steady state with
the increase in GDP per capita between the pre- and post-growth steady states. We perform
this same exercise for each economy in our study. Figure 6 plots the percent increase in
per capita GDP over this period and the increase that would have occurred from electricity
investments alone. Table 5 reports the percent of the observed increase in GDP per capita
explained by the expansions of grid-energy infrastructure.
21
Figure 6: GDP per Growth 2000-2013: Data and Model Counterfactual
140
Data
Model: Grid Energy Investment Only
Percent Explained
GDP Per Capita Growth: 2000−2013
120
100
80
60
40
20
0
−20
Congo
Ethiopia
Kenya
Nigeria
Sudan
Tanzania
Table 5: Percent of Growth Explained By Grid Energy Investment
Congo
Ethiopia
Kenya
Nigeria
Sudan
Tanzania
AVERAGE
-19.8
27.4
65.6
23.0
85.3
31.0
35.4
Expansions in grid-energy infrastructure explain approximately one third (35.4 percent) of
growth on average. Energy infrastructure plays a particularly important role in growth in
Sudan, explaining 85.3 percent of total growth. The model finds such a large role for energy
in Sudanese growth because the observed increase in electricity per capita between the preand post-growth periods was very large, exceeding the growth rate of per capita GDP by
almost a factor of four. Sudan’s story is mirrored in Kenya; large growth in Kenyan per
capita electricity consumption relative to growth in per capita GDP imply that expansions
in grid-energy infrastructure also explain over half (65.6 percent) of Kenyan growth.
Ethiopia has the largest observed percentage increases in both per capita GDP and electricity
consumption between the pre- and post-growth periods; per capita electricity consumption
increased by 205 percent and per capita GDP increased by 132 percent. The increase in
energy infrastructure explains 27.4 percent of Ethiopia’s growth over this period. While
this impact is substantial, it is considerably smaller then the model’s findings for Sudan and
22
Kenya. The main reason for this difference is that the growth of electricity per capita relative
to per capita GDP is much higher in Sudan and Kenya than in Ethiopia.
Nigeria and Tanzania experienced lower growth in per capita electricity consumption than
Ethiopia which was accompanied by lower growth in per capita GDP. These two effects are
partially offsetting and the overall contribution of grid-energy infrastructure investment to
growth in both these countries is similar to its contribution in Ethiopia. Grid-energy infrastructure expansions explain 23 percent of growth in Nigeria and 31 percent in Tanzania.
In contrast to the other economies in our study, the expansion of grid energy infrastructure
fails to explain any of the growth in the Congo. While the Congo did experience a modest
(12 percent) increase in electricity per capita between the pre- and post-growth periods, our
model predicts that all of this increase was driven by higher demand for energy instead of by
lower prices from more grid-energy infrastructure. In fact, matching Congolese growth in
per capita GDP and electricity consumption requires grid-energy infrastructure to decrease
by 15 percent. The lower infrastructure combined with the higher demand imply that the
price of energy in the post-growth steady state is 7.5 times higher than in the pre-growth
steady state.
Three basic channels drive our quantitative conclusions, and in particular the large importance of energy investments in Africa’s growth. First, grid-energy infrastructure in the initial
period was very low, with grid-energy investment less than one percent of GDP. The low existing levels of infrastructure combined with diminishing returns to other factors imply that
the marginal returns to grid-energy investment are very high. Second, there were large
increases in per capita electricity consumption between the pre- and post-growth periods,
ranging from 12 percent in the Congo to 205 percent in Ethiopia. Third, energy plays a
substantial role in non-agricultural production in Africa, accounting for approximately 10
percent of manufacturing GDP.
To assess the relative importance of each of these channels, we recalculate the percent
of growth explained by grid-energy investment when we (counterfactually) reduce each
channel, one at a time, by fifty percent. Table 6 reports the results from these counterfactual
exercises. To evaluate the impact of the first channel, low existing levels of infrastructure
combined with diminishing returns, we double the level of grid-energy investment in the
initial steady state. The results, reported in the third column of Table 6, indicate that the low
initial levels of infrastructure are a crucial part of the story; with twice as much infrastructure
in the pre-growth steady state, on average grid-energy investment only explains 10 percent
of growth as opposed to 35.4 percent in the baseline.
23
Table 6: Counterfactuals: Percent of Growth Explained by Grid Energy Investment
Counterfactuals
Country
Baseline Exp.
Double pre-growth I g
Halve I g growth
Halve pre-growth
Congo
-19.8
-8.3
-9.5
-21.9
Ethiopia
27.4
7.2
17.0
11.5
Kenya
65.6
20.3
38.7
29.2
Nigeria
23.0
7.4
13.9
10.1
Sudan
85.3
21.9
71.2
35.5
Tanzania
31.0
11.2
17.7
14.2
AVERAGE
35.4
10.0
24.8
13.1
To evaluate the impact of the second channel, the large increases in grid-energy infrastructure, we suppose that the growth rate of grid-energy infrastructure is half of the value we
calculated in the baseline experiment. We adjust the growth rate of non-energy TFP, A, to
ensure that the model still matches GDP per capita in the long-run steady state. The results,
reported in the fourth column of Table 6, indicate that in this counterfactual, grid-energy
investment is less important than in the baseline experiment, explaining 24.8 percent of
growth, on average.
Finally, to evaluate the importance of the third channel, the energy share, we recalibrate the
model to match an economy with an energy share of 0.05, half the value of the energy share
target we match in Section 4. The results, reported in the fifth column of Table 6, imply
when energy is half as important in production, the contribution of grid-energy investment
to growth is considerably smaller than in the baseline experiment, only 13.1 percent on
average.
Reducing the impact of each channel by fifty percent substantially reduces grid-energy investment’s contribution to Africa’s growth, implying that all three of the channels are important determinants of the role of grid-energy investment in overall growth. However,
increasing the level of grid-energy investment in the initial steady state has the largest impact on the results. This finding suggests grid-energy investment was so important to growth
in Sub-Saharan Africa over this period largely because existing levels of grid-energy infrastructure were extremely low.
24
pe E
Y
5.2. Sensitivity Analysis
We evaluate the sensitivity of our results with respect to two key energy-related parameters, the elasticity of substitution, ε and the distribution parameter, µ, in the CES production
function for the non-agricultural good (equation (4)). In the calibration (described in Section 4) we first choose a set of parameters, which includes ε directly from the data and the
empirical literature. Given these directly calibrated parameters, we choose a second set of
parameters, which includes µ, to ensure that certain moments in the model match their
values in the data. We repeat this procedure in the sensitivity analysis for ε; we recalibrate
the model for the higher value of ε to ensure that the moments in the model still match
their observed values in the data.
Table 7: Sensitivity Analysis: Percent of Growth Explained by Grid Energy Investment
Congo
Ethiopia
Kenya
Nigeria
Sudan
Tanzania
AVERAGE
Baseline experiment
-19.8
27.4
65.6
23.0
85.3
31.0
35.4
ε = 0.1, recalibrate
-17.3
28.2
61.0
22.9
87.9
31.2
35.6
µ = 10 × µ
-20.5
33.2
66.1
25.8
104.6
33.0
40.4
Table 7 reports the effects of doubling ε and recalibrating the model and of increasing µ
by one order of magnitude. Neither of these parameter changes substantially change the
results; doubling ε implies that grid-energy investment explains approximately one percentage point more growth than in the baseline experiment while increasing µ by one order
of magnitude implies that grid energy investment explains approximately five percentage
points more of growth. We conclude that our choice of ε per se doesn’t drive our quantitative
conclusions. As long as the model is calibrated to match energy’s share of non-agricultural
employment (of ten percent), the choice of ε, perhaps surprisingly, is not central to our
quantitative results.
6. Conclusions and Future Work
After decades of low or non-existent growth, Sub-Saharan Africa experienced a dramatic
increase in GDP growth starting around 2000. The economics literature does not yet agree
on why. This paper explores the role of energy investments, such as new power plants and
an expansion of the electricity grid, which also increased fairly dramatically since 2000.
These energy investments led to robust increases in electric power consumption in Africa,
and particularly in the countries that experienced the most rapid growth in GDP.
25
To help quantify the importance of energy investments on Africa’s recent growth, we build
a multi-sector model with energy inputs in production and non-homothetic preferences. We
use the model to help separate the role of increases in energy production on GDP per capita
from the reverse channel, running from GDP increases to greater energy demand. To do
so, we discipline the model’s preferences using data on non-agricultural, agricultural and
energy expenditures as a function of income. We then feed in the observed increases in
Africa’s energy production, and ask how much of Africa’s growth can be accounted for by
the energy increases alone.
In our main specification, around one-third of Africa’s growth in GDP per capita since 2000
can be attributed to its energy investments. The large quantitative importance of energy
investments is due in large part to three basic features of the data. First, Africa had extremely low levels of electricity consumption in 2000, at far less than one-percent of the
U.S. level. Second, electricity consumption increased dramatically since 2000, averaging
around eight percent growth per year on average. Third, energy plays an important role in
non-agricultural production in the developing world, with a share around ten percent.
In future work, we plan to incorporate richer preferences, like those of Boppart (2014)
or Comin, Lashkari, and Mestieri (2014), which allow for greater flexibility in matching
the cross-section of expenditure patterns than the restrictive Stone-Geary preferences used
currently. One limitation of our model so far is that it over-predicts the income elasticities
of energy (and non-agricultural goods). This may lead us to under-estimate the role of
electricity in driving Africa’s growth. We also plan to incorporate more direct data on energy
investments, and on energy capital more generally. These data can hopefully provide more
evidence with which to refine our quantitative conclusions.
26
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